Image Imported as plane not reflecting?
There's nothing wrong with the plane, it is reflecting unto your glossy floor, it's the angle of the camera and the fact that the floor is a perfect mirror that is misleading you to think it is just showing through and not reflecting.

To see this, try to change the base color of your glossy shader:



Or, you can change the roughness value of your glossy shader to something above 0, and see that the reflected bits are rough:



Give it a go and let us know if this is truly the case or if something weird is actually happening.